SOLUTION: Hello. I have a question that I can't understand how to solve. Any help would be appriciated. Thank you! Solve, graph on a number line and write your answer in set-builder no

Algebra ->  Inequalities -> SOLUTION: Hello. I have a question that I can't understand how to solve. Any help would be appriciated. Thank you! Solve, graph on a number line and write your answer in set-builder no      Log On


   

Question 187311: Hello. I have a question that I can't understand how to solve. Any help would be appriciated. Thank you!
Solve, graph on a number line and write your answer in set-builder notation.
- x/2 + 4 < 3x/2 + 8
It's - x over 2 and 3x over 2. I did not know how to do fractions on here so used the / sign.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-x%2F2%2B4%3C3x%2F2%2B8 Start with the given inequality.


Multiply EVERY term by the LCD 2 to clear the fractions.


-x%2B8%3C3x%2B16 Distribute and multiply.


-x%3C3x%2B16-8 Subtract 8 from both sides.


-x-3x%3C16-8 Subtract 3x from both sides.


-4x%3C16-8 Combine like terms on the left side.


-4x%3C8 Combine like terms on the right side.


x%3E%288%29%2F%28-4%29 Divide both sides by -4 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E-2 Reduce.


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Answer:

So the answer is x%3E-2



The answer in interval notation is


Also, the answer in set-builder notation is


Here's the graph of the solution set on a number line: